Mathematics, 10.01.2021 14:00 skyemichellec

What is an equation of the line that passes through the point (6,−4) and is perpendicular to the line 2x−y=5?

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Answer from: zakeiryh

An equation of the line that passes through the point (6,−4) and is perpendicular to the line 2x−y=5 is $y=-\frac{1}{2}x-1$

Given:

An equation of the line that passes through the point (6,−4) and is perpendicular to the line 2x−y=5

First we find the slope of given equation 2x-y=5

y=mx+b is the equation of the line . where 'm' is the slope

$2x-y=5\\2x-5=y\\y=2x-5$

Slope m=2.

Slope of perpendicular lines are negative reciprocal of one another

Slope of perpendicular line is $-\frac{1}{2}$

The line passes through the point (6,-4)

Use the point and slope to get the equation of the perpendicular line

slope m = $-\frac{1}{2}$

Point slope form of line is

$y-y_1=m(x-x_1)\\y+4=-\frac{1}{2}(x-6)\\y+4=-\frac{1}{2}x+3\\y=-\frac{1}{2}x-1$

An equation of the line that passes through the point (6,−4) and is perpendicular to the line 2x−y=5 is $y=-\frac{1}{2}x-1$

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Answer from: wowihavefun

An equation of the line that passes through the point (6,−4) and is perpendicular to the line will be:

$y=-\frac{1}{2}x-1$

Step-by-step explanation:

We know that the slope-intercept form of the line equation

y = mx+b

where m is the slope and b is the y-intercept

Given the line

2x-y=5

converting the line into slope-intercept form

y = 2x-5

comparing with the slope-intercept form of the line equation

The slope of the line = m = 2

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:

slope = m = 2

Thus, the equation of new line = – 1/m = -1/2 = -1/2

using the point-slope form of the line equation

$y-y_1=m\left(x-x_1\right)$

where m is the slope of the line and (x₁, y₁) is the point

substituting the values of the slope = -1/2 and the point (6,−4)

$y-\left(-4\right)=-\frac{1}{2}\left(x-6\right)$

$y+4=-\frac{1}{2}\left(x-6\right)$

Subtract 4 from both sides

$y+4-4=-\frac{1}{2}\left(x-6\right)-4$

$y=-\frac{1}{2}x-1$

Therefore, an equation of the line that passes through the point (6,−4) and is perpendicular to the line will be:

$y=-\frac{1}{2}x-1$

Answer from: Quest

an advantage of the standard deviation is that it increases as the dispersion of the data increases. e. the interquartile range is preferred when the data are not skewed or no have outliers. an advantage of the standard deviation is that it uses all the observations in its computation.

Answer from: Quest

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